Document Type
Article
Publication Date
4-1-2013
Abstract
In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ℝ × ℝ with d ≥ 6. We prove the stability of solutions under the weak condition that the perturbation of the linear flow is small in certain space-time norms. As a by-product of our stability analysis, we also prove local well-posedness of solutions for which we only assume the smallness of the linear evolution. These results provide essential technical tools that can be applied towards obtaining the extension to high dimensions of the analysis of Kenig and Merle [17] of the dynamics of the focusing (NLW) below the energy threshold. By employing refined paraproduct estimates we also prove unconditional uniqueness of solutions for d ≥ 6 in the natural energy class. This extends an earlier result by Planchon [26]. © 2013 Copyright Taylor and Francis Group, LLC. d
Publication Source (Journal or Book title)
Communications in Partial Differential Equations
First Page
575
Last Page
607
Recommended Citation
Bulut, A., Czubak, M., Li, D., Pavlović, N., & Zhang, X. (2013). Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions. Communications in Partial Differential Equations, 38 (4), 575-607. https://doi.org/10.1080/03605302.2012.756520